Westonci.ca is the Q&A platform that connects you with experts who provide accurate and detailed answers. Experience the ease of finding accurate answers to your questions from a knowledgeable community of professionals. Discover detailed answers to your questions from a wide network of experts on our comprehensive Q&A platform.
Sagot :
To determine the number of solutions for the given system of linear equations, we need to analyze both equations and compare their slopes and y-intercepts.
The given system of linear equations is:
[tex]\[ \begin{array}{l} y = -4x - 5 \\ y = -4x + 1 \end{array} \][/tex]
Let's break this down step-by-step:
1. Identify the slopes of both equations:
- The slope of the first equation [tex]\( y = -4x - 5 \)[/tex] is [tex]\(-4\)[/tex].
- The slope of the second equation [tex]\( y = -4x + 1 \)[/tex] is also [tex]\(-4\)[/tex].
2. Compare the slopes:
- Both equations have the same slope of [tex]\(-4\)[/tex].
3. Identify the y-intercepts of both equations:
- The y-intercept of the first equation [tex]\( y = -4x - 5 \)[/tex] is [tex]\(-5\)[/tex].
- The y-intercept of the second equation [tex]\( y = -4x + 1 \)[/tex] is [tex]\(1\)[/tex].
4. Compare the y-intercepts:
- The y-intercepts are different ([tex]\(-5\)[/tex] and [tex]\(1\)[/tex]).
Since the slopes are the same but the y-intercepts are different, the lines represented by these equations are parallel. Parallel lines never intersect, so there is no point that satisfies both equations simultaneously.
As a result, the system of equations has:
No solution
So, you should match the given system of equations with "No solution".
The given system of linear equations is:
[tex]\[ \begin{array}{l} y = -4x - 5 \\ y = -4x + 1 \end{array} \][/tex]
Let's break this down step-by-step:
1. Identify the slopes of both equations:
- The slope of the first equation [tex]\( y = -4x - 5 \)[/tex] is [tex]\(-4\)[/tex].
- The slope of the second equation [tex]\( y = -4x + 1 \)[/tex] is also [tex]\(-4\)[/tex].
2. Compare the slopes:
- Both equations have the same slope of [tex]\(-4\)[/tex].
3. Identify the y-intercepts of both equations:
- The y-intercept of the first equation [tex]\( y = -4x - 5 \)[/tex] is [tex]\(-5\)[/tex].
- The y-intercept of the second equation [tex]\( y = -4x + 1 \)[/tex] is [tex]\(1\)[/tex].
4. Compare the y-intercepts:
- The y-intercepts are different ([tex]\(-5\)[/tex] and [tex]\(1\)[/tex]).
Since the slopes are the same but the y-intercepts are different, the lines represented by these equations are parallel. Parallel lines never intersect, so there is no point that satisfies both equations simultaneously.
As a result, the system of equations has:
No solution
So, you should match the given system of equations with "No solution".
We hope you found what you were looking for. Feel free to revisit us for more answers and updated information. Thank you for choosing our platform. We're dedicated to providing the best answers for all your questions. Visit us again. Your questions are important to us at Westonci.ca. Visit again for expert answers and reliable information.